Computational existence proofs for spherical <Emphasis Type=Italic>t</Emphasis>-designs

Spherical t-designs provide quadrature rules for the sphere which are exact for polynomials up to degree t. In this paper, we propose a computational algorithm based on interval arithmetic which, for given t, upon successful completion will have proved the existence of a t-design with (t + 1)² nodes on the unit sphere S² ì mathbbR³{S^2 subset mathbb{R}^3} and will have computed narrow interval enclosures which are known to contain these nodes with mathematical certainty. Since there is no theoretical result which proves the existence of a t-design with (t + 1)² nodes for arbitrary t, our method contributes to the theory because it was tested successfully for t = 1, 2, . . . , 100. The t-design is usually not unique; our method aims at finding a well-conditioned one. The method relies on computing an interval enclosure for the zero of a highly nonlinear system of dimension (t + 1)². We therefore develop several special approaches which allow us to use interval arithmetic efficiently in this particular situation. The computations were all done using the MATLAB toolbox INTLAB.     

On Preconditioners for the Borsuk Existence Test

Existence or fixed point theorems, combined with interval analytic methods, provide a means to computationally prove the existence of a zero of a nonlinear system in a given interval vector. One such test is based on Borsuk's existence theorem. We discuss preconditioning techniques that are aimed at improving the effectiveness of this test. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetische Resonanz-Studien der Eigenschaften von Wasser in Celluloseacetat-Membranen

Ohne Zusammenfassung     

Chemical effects on Al and Cu Auger electron spectra for the intermetallic compound CuAl2

This paper describes an experimental study of the intermetallic compound CuAl₂ using Auger electron spectroscopy (AES). Chemical effects in the CuAl₂ spectrum are observed corresponding to energy shifts of the Cu and Al peaks and the appearance of a new peak for the compound. These results are found to be in good agreement with those obtained using the technique of soft X-ray emission spectroscopy (SXES). The origin of the new peak appears to be a transition from a hybridised s-d band localized at the Cu site in the compound to an Al core state. This gives a band-like contribution to the CuAl₂ AES spectrum.     

Chemistry and Biochemistry of Microbial α-Glucosidase Inhibitors

α-Glucosidases are among the most important carbohydrate-splitting enzymes. They catalyze the hydrolysis of α-glucosidic linkages. Their substrates are—depending on their specificity—oligo- and polysaccharides. Microbial inhibitors of α-amylases and other mammalian intestinal carbohydrate-splitting enzymes studied during the last few years have aroused medical interest in the treatment of metabolic diseases such as diabetes. Moreover, they extend the spectrum of microbial secondary metabolites which comprises an enormous variety of structures. They also contribute considerably to a better understanding of the mechanism of action of α-glucosidases. These inhibitors belong to different classes of substances. Those studied most thoroughly are microbial α-glucosidase inhibitors which are members of a homologous series of pseudooligosaccharides of the general formula (4). They all have a core in common which is essential for their inhibitory action, a pseudodisaccharide residue consisting of an unsaturated cyclitol unit, and a 4-amino-4,6-dideoxy- glucose unit. The—in many respects—most interesting representative of this homologous series is acarbose (5), a pseudotetrasaccharide exhibiting a very pronounced inhibitory effect on intestinal α-glucosidases such as sucrase, maltase and glucoamylase. The present paper will review this new field of microbial α-glucosidase inhibitors which has been studied with particular intensity during the past ten years.     

Direct modulation and optical confinement factor modulation of semiconductor lasers

A method for modulation of semiconductor lasers is demonstrated. The method is based on the modulation of the optical confinement factor. Using this method an enhanced—3-dB bandwidth is observed in agreement with the small signal rate equation analysis. A modulation response that drops at high frequencies slower than the conventional direct current modulation response is achieved. This supports the theoretical predictions, showing an intrinsic 1/f decay rate for the optical confinement factor modulation scheme versus an intrinsic 1/f² decay for direct modulation.